1. Field of the Invention
The present invention relates to the measurement, characterization, and simulation of aberrations of lithography projection systems.
2. Description of the Related Art
During semiconductor wafer processing, optical projection lithography is typically used to print fine integrated circuit patterns onto semiconductor wafers. As illustrated in FIG. 1, optical projection lithography utilizes a light source, a patterned mask, an optical system including elements such as projection lenses, mirrors, etc., and a semiconductor wafer coated with a thin layer of photoresist. The projected mask pattern is reduced in size by the optical system, typically by a factor of approximately four, and imaged onto the photoresist. The mask pattern of light and shadow imaged onto the photoresist causes chemical reactions which alter the photoresist that, together with additional processing steps, creates an identical, yet reduced in size, pattern of features on the wafer. The patterned photoresist layer then serves as a template on the semiconductor wafer for subsequent processing steps.
As lithography technology has advanced, optical projection lithography has achieved further reductions of feature sizes and increases of feature densities across the semiconductor wafer surface. These advancements have included better resolution by reducing the wavelength of the light used for imaging, tighter process controls, and improvements of the optical systems, processing equipment, and masks.
Elements of lithography optical systems are invariably manufactured with some degree of errors or aberrations. As the limit of optical lithography is pushed and feature densities continue to increase, pattern placement errors due to the aberrations become increasingly more important. Left uncorrected, these aberrations create distortions of the mask pattern on the wafer, resulting in mispositioning or misshaping of the various features across the wafer. However, once the aberrations of a particular optical system are known, masks can be designed so that the resulting features on the wafer have the desired positions and shapes.
Interferometry has been used for many years to characterize the aberrations of optical lithography lenses. However, these interferometry measurements must be performed before the lens is mounted into the optical system. It is therefore more desirable to utilize another method to quantify the optical aberrations which can be performed xe2x80x9cin-linexe2x80x9d (i.e., using product wafers themselves as they emerge from the lithography process, rather than performing some specialized test method or using a specialized test piece).
One method to mathematically model aberrations utilizes Zernike polynomials, which are a complete orthogonal set of polynomials over the interior of the unit circle. The Zernike series representation is useful for providing explicit expressions for the well-known low-order aberrations such as coma, astigmatism, etc. Generally, the Zernike coefficients Zn of the higher-order polynomials are less significant in the description of aberrations than are the lower-order coefficients. However, as feature sizes continue to shrink, a few of the higher-order coefficients are becoming increasingly more important in semiconductor processing. These higher-order coefficients include Z7 (third-order X coma), Z8 (third-order Y coma), Z9 (third-order spherical), Z10 (third-order three-leaf), Z14 (fifth-order X coma), and Z15 (fifth-order Y coma). For example, H. Fukuda, et al., xe2x80x9cDetermination of High-Order Lens Aberration Using Phase/Amplitude Linear Algebra,xe2x80x9d 43rd Int""l Conf. on Electron, Ion, and Photo Beam Technology and Nanofabrication, June 1999 discloses the use of side-lobe intensity measurements taken near the pattern edge of attenuated phase-shifting masks to detect higher-order aberrations. It is such coma aberrations, which can be characterized using Z7 and Z14 coefficients, which have been assumed to give rise to misaliginnents between the center digit line contact and the left and right storage node contacts of an exemplary DRAM circuit design during photolithography processes at wavelengths of 248 nm and 193 nm.
In accordance with one aspect of the present invention, a method is provided for determining a value of an effective three-leaf aberration coefficient of an actual photolithography system. The method comprises measuring at least two dimensions of a photolithography pattern produced by the actual photolithography system, and calculating an asymmetry from the two measured dimensions. The method further comprises calculating the value of the effective three-leaf aberration coefficient corresponding to the calculated asymmetry.
In accordance with another aspect of the present invention, a method is provided for determining a value of an effective three-leaf aberration coefficient of an actual photolithography system. The method comprises measuring a first space between a left storage node contact and a center digit line contact of a dynamic random access memory array, and measuring a second space between a right storage node contact and the center digit line contact of the dynamic random access memory array. The method further comprises calculating an asymmetry between the first space and the second space, and calculating the value of the effective three-leaf aberration coefficient corresponding to the calculated asymmetry.
In accordance with another aspect of the present invention, a method is provided for determining a value of an effective three-leaf aberration coefficient of an actual photolithography system. The method comprises measuring a first space between a left feature and a center feature, the left and center features imaged by the actual photolithography system. The method further comprises measuring a second space between a right feature and the center feature, the right feature imaged by the actual photolithography system. The method further comprises calculating an asymmetry between the first space and the second space, and calculating the value of the effective three-leaf aberration coefficient corresponding to the calculated asymmetry.